Maharaj, Sunil Dutt.Govender, Gabriel.2017-02-072017-02-0720102010http://hdl.handle.net/10413/14036Doctor of Philosophy in Applied Mathematics. University of KwaZulu-Natal, Westville 2010.In this dissertation we construct radiating models for dense compact stars in relativistic astrophysics. We first utilise the standard Santos (1985) junction condition to model Euclidean stars. By making use of the heuristic Euclidean condition and a linear transformation in the gravitational potentials, we generate a particular exact solution in closed form to the nonlinear stellar boundary condition. Earlier models of spherical nonadiabatic gravitational collapse are then extended by considering the effect of radial perturbations in the matter and metric variables, on the evolution of the stellar fluid and the dynamics of the collapse process. The governing equation describing the temporal behaviour of the model is solved on the stellar surface. The model becomes static in the later stages of collapse. The Santos junction condition is then generalised to describe a radiating star which has a two-fluid atmosphere, consisting of a radiation field and a string fluid. We show that in the appropriate limit when the string energy density goes to zero, the standard result is regained. An exact solution to the generalised boundary condition is found. The generalised boundary condition is extended to hold in the case when the shear is nonvanishing. We demonstrate that our results can be used to model the flow of a string fluid in terms of a diffusion transport process.en-ZAAstrophysics.Stars.Theses--Applied mathematics.Thesis